The revelations have reignited concerns about the safety of Britain's nuclear stations. French-owned EDF Energy admitted that it had not followed the correct procedures, but insisted that there had been no danger to the public.

In one incident, an equipment malfunction cut off the electricity supplied to a gas circulator. Gas circulators are critical components because they ensure that air is kept moving to cool reactor fuel and prevent it from overheating.

The second incident also involved problems with electricity supply, though this time to a radioactive fuel dismantling facility at Torness. According to EDF Energy, the two events were "entirely unconnected".

The NII report says: "The events included contributions from operators not complying in full with the instructions provided to ensure safe limits and conditions are observed during plant operations."

Nuclear inspectors have written to EDF Energy requiring more information about the incidents, and have received a response. The NII is satisfied there is "no immediate safety issue" but has left open the possibility of taking enforcement action in the future.

The report, which covers the final three months of 2010, also reveals that one Torness reactor had "several unplanned shutdowns, requiring action to correct adverse conditions which affected operation of the reactor". This happened after the reactor had restarted after a planned maintenance shutdown.

In addition, the second reactor at Torness had to be manually shut down because the screens that take in seawater for cooling were blocked by a large mass of seaweed. Inspectors identified "a number of areas where further enhancement may be possible" in the safety arrangements for dealing with seaweed.

"These are all events that should ring very loud alarm bells," said Pete Roche, an Edinburgh-based nuclear consultant and editor of the no2nuclearpower.org.uk website. "As we've seen with Three Mile Island, Chernobyl and now Fukushima, a combination of unexpected events all happening at once can quickly lead to a serious accident because of the highly dangerous nature of the fuel used to power these reactors."

The Scottish Nationalist MSP, Shirley-Anne Somerville, said: "EDF Energy must confirm that these issues have been resolved and that they have every measure in place to make sure there are no further problems at the plant."

She added: "The SNP's opposition to nuclear power has been long held and while there are nuclear power stations operating in Scotland we must take every possible step to ensure their safety."

The director of Torness, Paul Winkle, argued that the company had a good safety record and welcomed input by the NII. The problems with electricity supplies to the gas circulators occurred because "one piece of a group of equipment failed", he said.

"While power to one gas circulator was removed, others operated as normal, as they are designed to do, and there was, therefore, no possibility of losing cooling."

The issue with power supplies to the radioactive fuel dismantling facility was reported to the NII because "we hadn't followed procedure exactly as we should", he added.

According to Winkle, the seaweed blockage had been predicted by "sophisticated monitoring systems". None of the incidents had caused any danger to staff, plant or the public, he insisted.

• This article was changed on 23 March - "the last three months of 2010" now reads "in September last year".